I've never actually had a pie from either place but I've seen pics and read info on it before and I think it's done with cheddar, either yellow or white, around the rim of the crust. In contact with the pan it will fry up real good and the heavy amount of oil from cheddar will run down into the crust or along the wall of the pan to the bottom. Again, I'm not certain that's how it's done, but it may be worth a try for you.

I've tried it, it worked for me and my family loved it, i started out by making a chi deep dish, but was having trouble keeping the sides of the crust to stay up, so i said F-it and put my sliced mozzarella up along the sides of the pan them just added the sauce, same as chi-style, just dont pull up the sides, hope you found this helpful

Basically, caramelized crust is brown/burnt cheese or a combination of cheese and sauce that attaches itself to the outer pizza crust.

You get this by:1) Pressing your dough out not entirely to the edge of your pizza pan. Leave a little gap between the dough and the inside of the pan. If your dough has natural springback, it's not an issue, so sometimes it's good to use cold dough for this.

2) Hang your sliced cheese (mozzarella, wisconsin brick, mild cheddar) so part of it leans up against the inside of the pan.This gives it a chance to run down between the dough and the pan.

3) Spread your sauce out as far as you can so a little bit can also follow the cheese down the gap.